Would engaging in war with 'Amalek without a specific command (a la Shaul) be a Milhemeth Mitzvah or Milhemeth Reshuth?

Is killing all of 'Amalek (as opposed to assimilating them, perhaps) a Mitzvah, or a Reshuth? If you had a choice, is total physical annihilation preferred over peacefully (or even forcefully) converting them all?